Geodesic
Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 616-627

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We prove pointwise gradient bounds for entire solutions of pde's of the form      ℒu(x) = ψ(x, u(x), ∇u(x)), where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.

DOI : 10.1051/cocv/2012024
Classification : 35J60, 35B45
Keywords: gradient bounds, P-function estimates, rigidity results 
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     author = {Farina, Alberto and Valdinoci, Enrico},
     title = {Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {616--627},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {2},
     year = {2013},
     doi = {10.1051/cocv/2012024},
     mrnumber = {3049726},
     zbl = {1273.35126},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012024/}
}
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Farina, Alberto; Valdinoci, Enrico. Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 616-627. doi: 10.1051/cocv/2012024

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